Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings

By Wataru Takahashi, Masashi Toyoda. 2003

686 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/45cc021c800f1260714aa08a134890ec4372288a

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In Civil and Structural Engineering

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

STRONG CONVERGENCE THEOREM BY AN EXTRAGRADIENT METHOD FOR FIXED POINT PROBLEMS AND VARIATIONAL INEQUALITY PROBLEMS (2006, background): “For finding an element of F (S) ∩ Ω under the assumption that a set C ⊂ H is nonempty, closed and convex, a mapping S : C → C is nonexpansive and a mapping A : C → H is α-inverse-strongly-monotone, Takahashi and Toyoda [8] introduced the following iterative scheme: xn+1 = αnxn + (1− αn)SPC(xn − λnAx”
New Methods with Perturbations for Non-Expansive Mappings in Hilbert Spaces (2011, background): “Recently, iterative methods for finding fixed points of non-expansive mappings have received vast investigations due to its extensive applications in a variety of applied areas of inverse problem, partial differential equations, image recovery, and signal processing; see [1-34] and the references th”
Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings (2005, neutral): “We also have that for all x, y ∈ C and λ > 0, (3) So, if λ ≤ 2α, then I − λA is a nonexpansive mapping of C into H. Proposition 2.1[7] Let C be a bounded closed convex subset of a real Hilbert space H and let A be an α inverse strongly-monotone mapping of C into H.”
Fixed Point Theorems and Weak Convergence Theorems for Generalized Hybrid Mappings in Hilbert Spaces (2010, neutral): “W. Takahashi and M. Toyoda, Weak convergence theorems for nonexpansive mappings and monotone mappings, J. Optim.”
Weak Convergence Theorem by an Extragradient Method for Variational Inequality, Equilibrium and Fixed Point Problems (2009, methodology): “To find an element of F (S) ∩ V I(A,C), Takahashi and Toyoda [11] introduced the following iterative scheme:”
An efficient iterative method for finding common fixed point and variational inequalities in Hilbert spaces (2018, background): “Takahashi and Toyoda [29] presented the following algorithm for solving (4).”
A new hybrid iterative method for solution of equilibrium problems and fixed point problems for an inverse strongly monotone operator and a nonexpansive mapping (2009, methodology): “Generally speaking, the algorithm suggested by Takahashi and Toyoda [ 22 ] is based on two well-known types of methods, namely, on the projection-type methods for solving variational inequality problems and so-called hybrid or outer-approximation methods for solving fixed point problems.”
Weak and Strong Convergence Theorems for a Nonexpansive Mapping and an Equilibrium Problem (2007, methodology): “In this section, we consider a weak convergence theorem motivated by [ 9 ].”
Parallel Hybrid Iterative Methods for Variational Inequalities, Equilibrium Problems, and Common Fixed Point Problems (2015, methodology): “Takahashi and Toyoda [19] proposed a weakly convergent method for finding P. K. Anh (Corresponding author) · D.V. Hieu College of Science, Vietnam National University, Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam E-mail: anhpk@vnu.edu.vn, dv.hieu83@gmail.com a common element of the set of fixe”